# ,070

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## FV1 = P0 (1 + i)1 = \$1,000 (1.07) = \$1,070

• FV1 = P0 (1 + i)1 = \$1,000 (1.07) = \$1,070
• FV2 = FV1 (1 + i)1 = P0 (1 + i)(1 + i) = \$1,000(1.07)(1.07) = P0 (1 + i)2 = \$1,000(1.07)2 = \$1,144.90
• You earned an EXTRA \$4.90 in Year 2 with compound over simple interest.
• Future Value
• Single Deposit (Formula)

## General Future Value Formula

• FV1 = P0(1 + i)1
• FV2 = P0(1 + i)2
• General Future Value Formula:
• FVn = P0 (1 + i)n
• or FVn = P0 (FVIFi,n) – See Table I
• etc.

## Valuation Using Table I

• FVIFi,n is found on Table I
• at the end of the book.

## Using Future Value Tables

• FV2 = \$1,000 (FVIF7%,2) = \$1,000 (1.145) = \$1,145 [Due to Rounding]

## TVM on the Calculator

• N: Number of periods
• I/Y: Interest rate per period
• PV: Present value
• PMT: Payment per period
• FV: Future value
• CLR TVM: Clears all of the inputs into the above TVM keys

## Using The TI BAII+ Calculator

• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• Focus on 3rd Row of keys (will be displayed in slides as shown above)

## Entering the FV Problem

• Press:
• 2nd CLR TVM
• 2 N
• 7 I/Y
• –1000 PV
• 0 PMT
• CPT FV
• Source: Courtesy of Texas Instruments

## Solving the FV Problem

• N: 2 Periods (enter as 2)
• I/Y: 7% interest rate per period (enter as 7 NOT 0.07)
• PV: \$1,000 (enter as negative as you have “less”)
• PMT: Not relevant in this situation (enter as 0)
• FV: Compute (Resulting answer is positive)
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 2 7 –1,000 0
• 1,144.90

## Story Problem Example

• Julie Miller wants to know how large her deposit of \$10,000 today will become at a compound annual interest rate of 10% for 5 years.
• 0 1 2 3 4 5
• \$10,000
• FV5
• 10%

## Story Problem Solution

• Calculation based on Table I: FV5 = \$10,000 (FVIF10%, 5) = \$10,000 (1.611) = \$16,110 [Due to Rounding]
• Calculation based on general formula: FVn = P0 (1 + i)n FV5 = \$10,000 (1 + 0.10)5 = \$16,105.10

## Entering the FV Problem

• Press:
• 2nd CLR TVM
• 5 N
• 10 I/Y
• –10000 PV
• 0 PMT
• CPT FV
• Source: Courtesy of Texas Instruments

## Solving the FV Problem

• The result indicates that a \$10,000 investment that earns 10% annually for 5 years will result in a future value of \$16,105.10.
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 5 10 –10,000 0
• 16,105.10

• We will use the “Rule-of-72”.
• Quick! How long does it take to double \$5,000 at a compound rate of 12% per year (approx.)?

## The “Rule-of-72”

• Approx. Years to Double = 72 / i%
• 72 / 12% = 6 Years
• [Actual Time is 6.12 Years]
• Quick! How long does it take to double \$5,000 at a compound rate of 12% per year (approx.)?

## Solving the Period Problem

• The result indicates that a \$1,000 investment that earns 12% annually will double to \$2,000 in 6.12 years.
• Note: 72/12% = approx. 6 years
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 12 –1,000 0 +2,000
• 6.12 years

## Present Value Single Deposit (Graphic)

• Assume that you need \$1,000 in 2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually.
• 0 1 2
• \$1,000
• 7%
• PV1
• PV0

## PV0 = FV2 / (1 + i)2 = \$1,000 / (1.07)2 = FV2 / (1 + i)2 = \$873.44

• PV0 = FV2 / (1 + i)2 = \$1,000 / (1.07)2 = FV2 / (1 + i)2 = \$873.44
• 0 1 2
• \$1,000
• 7%
• PV0
• Present Value Single Deposit (Formula)

## PV0 = FV1 / (1 + i)1

• PV0 = FV1 / (1 + i)1
• PV0 = FV2 / (1 + i)2
• General Present Value Formula:
• PV0 = FVn / (1 + i)n
• or PV0 = FVn (PVIFi,n) – See Table II
• etc.
• General Present Value Formula
• Valuation Using Table II
• PV2 = \$1,000 (PVIF7%,2) = \$1,000 (.873) = \$873 [Due to Rounding]
• Using Present Value Tables
• N: 2 Periods (enter as 2)
• I/Y: 7% interest rate per period (enter as 7 NOT 0.07)
• PV: Compute (Resulting answer is negative “deposit”)
• PMT: Not relevant in this situation (enter as 0)
• FV: \$1,000 (enter as positive as you “receive \$”)
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 2 7 0 +1,000
• –873.44
• Solving the PV Problem

## Julie Miller wants to know how large of a deposit to make so that the money will grow to \$10,000 in 5 years at a discount rate of 10%.

• Julie Miller wants to know how large of a deposit to make so that the money will grow to \$10,000 in 5 years at a discount rate of 10%.
• 0 1 2 3 4 5
• \$10,000
• PV0
• 10%
• Story Problem Example

## Calculation based on general formula: PV0 = FVn / (1 + i)n PV0 = \$10,000 / (1 + 0.10)5 = \$6,209.21

• Calculation based on general formula: PV0 = FVn / (1 + i)n PV0 = \$10,000 / (1 + 0.10)5 = \$6,209.21
• Calculation based on Table I: PV0 = \$10,000 (PVIF10%, 5) = \$10,000 (0.621) = \$6,210.00 [Due to Rounding]
• Story Problem Solution
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 5 10 0 +10,000
• –6,209.21
• The result indicates that a \$10,000 future value that will earn 10% annually for 5 years requires a \$6,209.21 deposit today (present value).
• Solving the PV Problem

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